i came across while looking into a narrow tire vs. a wide tire. the argument was that the wider tire, due to more surface area acting on the other material (ground), would have more traction because there was more grabbing potential.

this statement in fact if false and heres a good little read about frictions and such.

"A wonderful example of "In theory there is no difference between theory and reality. In reality however, there is."

The total friction may be the same, but there will always be more available traction offroad with a narrower tire. It's about loading, a larger footprint has a lower pressure on the ground for each square inch of the contact patch, therefore is easier to break loose. You will do much better in mud and dirt with skinnies - they dig down in mud and may better find something to bite on, and on dirt or whathaveyou they put more weight on the tread to get grip and keep you moving. With harder surfaces it can go either way. In sand, the narrower tire's better bite will dig holes - not good. So wider - assuming you get wide enough to provide some flotation - will probably be better. On snow, narrower tires give a better bite and better traction - but in Deep snow, wide enough to provide flotation might be best (gotta go REAL wide though!) Also note that larger diameter tires increase the footprint too, and mathematically/geometrically allow for a better climbing, final gearing being the same. Whether wide tires or narrower tires are better for your type of wheeling is the issue each has to decide. Like most things, there is no "best" answer - it's all relevant."

In theory, friction is only dependent on coefficient of friction (determined by the materials in contact) and normal force (load pushing the two together).

In the real world, a smaller contact patch will "lose grip" under less total force because the rubber in the tire will reach its critical shearing stress at a lower total force acting through it, although tread patterns and shapes can factor in as well. Unless you're supporting weight with the steel in the tires (which in my experience is rarely good for tire life), the contact patch area will be the weight supported by a particular wheel (normal force) divided by tire pressure regardless of the width of the tire you're using.

The reason for a narrower tire's "bite" or a wider tire's "float" will be due to the tendency to have higher pressure in the narrower ones and lower pressure in wider to control tire deformation (and the "rolling friction" and tire wear & tear that comes with it) during street driving, but with durable enough sidewalls, there's nothing to stop one from running 165s at 20 psi and develop the same size contact patch as 255s at the same pressure; the other thing about wider tires is that more of that bigger patch would consist of the treadwall as opposed to flexed out sidewall.